Tuning-fork resonator with grooves on principal surfaces

ABSTRACT

A resonator element includes: a base part; and a resonating arm part that extends from the base part in a first direction and performs flexing vibration, wherein the resonating arm part has one principal surface and the other principal surface opposed to the one principal surface, a first groove part provided along the first direction of the resonating arm part on the one principal surface, a second groove part provided in juxtaposition with the first groove part in a second direction orthogonal to the first direction in a plan view on the other principal surface, a third groove part provided in juxtaposition with the first groove part in the first direction in the plan view and provided nearer the base part side than the first groove on the other principal surface, and a fourth groove part provided in juxtaposition with the second groove part in the first direction in the plan view and provided nearer the base part side than the second groove on the one principal surface, and wherein a sum of a depth of the first groove part and a depth of the second groove part and a sum of a depth of the third groove part and a depth of the fourth groove part are larger than a distance between the one principal surface and the other principal surface.

BACKGROUND

1. Technical Field

The present invention relates to a resonator element, a resonator, anoscillator, and an electronic apparatus.

2. Related Art

In related art, it is known that, as a piezoelectric resonator elementas an example of a resonator element is made smaller, the Q factorbecomes smaller and vibration is hindered.

Specifically, in the piezoelectric resonator element, with elasticdeformation due to flexing vibration, the temperature of the contractingsurface rises and the temperature of the expanding surface falls, and atemperature difference is produced within. Thereby, in the piezoelectricresonator element, vibration called relaxation oscillation occurs ininverse proportion to a required time (relaxation time) until thetemperature difference is eliminated (temperature equilibration) bythermal conduction (heat transfer).

As the piezoelectric resonator element is made smaller, the frequency ofthe relaxation oscillation and the frequency of the original flexingvibration come closer, and a phenomenon that the Q factor becomessmaller and the original flexing vibration is hindered occurs.

This phenomenon is called thermoelastic loss or thermoelastic effect,and, as measures therefor, in JP-UM-A-2-32229, a groove or a throughhole is formed in the rectangular section of the piezoelectric resonatorelement to suppress the heat transfer from the contracting surface tothe expanding surface, and thereby, reduction of the Q factor caused bythermoelastic loss is suppressed.

However, if a through hole is formed in the vibrating part (hereinafter,referred to as “resonating arm part”) of the piezoelectric resonatorelement as in JP-UM-A-2-32229, there is a problem that the stiffness ofthe resonating arm part is significantly reduced.

Further, if the piezoelectric resonator element is provided with anH-shaped groove (hereinafter, referred to as “groove part”) in theresonating arm part as in JP-UM-A-2-32229, the suppression of the heattransfer from the contracting surface to the expanding surface isinsufficient and there is room for improvement in suppression of thereduction of the Q factor caused by thermoelastic loss.

SUMMARY

An advantage of some aspects of the invention is to solve at least apart of the problems mentioned above and the invention can be embodiedas the following embodiments or application examples.

Application Example 1

A piezoelectric resonator element according to this application exampleincludes a base part, and a resonating arm part that extends from thebase part and performs flexing vibration, wherein the resonating armpart has one principal surface and the other principal surface opposedto the one principal surface, a first groove part formed along anextension direction of the resonating arm part on the one principalsurface, a second groove part formed in parallel with the first groovepart in a plan view on the other principal surface, a third groove partformed in series with the first groove part in the plan view nearer thebase part side than the first groove part on the other principalsurface, and a fourth groove part formed in series with the secondgroove part in the plan view nearer the base part side than the secondgroove part on the one principal surface, and wherein a sum of a depthof the first groove part and a depth of the second groove part and a sumof a depth of the third groove part and a depth of the fourth groovepart are larger than a distance between the one principal surface andthe other principal surface.

According to the configuration, the piezoelectric resonator element hasthe first groove part on the one principal surface and the second groovepart formed in parallel with the first groove part on the otherprincipal surface. Further, the piezoelectric resonator element has thethird groove part formed in series with the first groove part nearer thebase part than the first groove part on the other principal surface, andthe fourth groove part formed in series with the second groove partnearer the base part than the second groove part on the one principalsurface.

Further, in the piezoelectric resonator element, the sum of the depth ofthe first groove part and the depth of the second groove part and thesum of the depth of the third groove part and the depth of the fourthgroove part are larger than the distance between the one principalsurface and the other principal surface.

Thereby, in the piezoelectric resonator element, for example, comparedto the case where groove parts having H-shaped sections are provided inthe resonating arm part as in related art, the distance of heat transferfrom one of the pair of contracting and expanding surfaces as acontracting surface in the flexing vibration to the other of the pair ofcontracting and expanding surfaces as an expanding surface are longer,and thus, the relaxation time until the temperature equilibration isachieved becomes longer.

As a result, regarding the piezoelectric resonator element, thefrequency of the relaxation oscillation is made farther from thefrequency of the original flexing vibration, and the reduction of the Qfactor due to thermoelastic loss can be suppressed. Therefore, thepiezoelectric resonator element can be further downsized.

Now, in the piezoelectric resonator element, the sectional shapecontaining the first groove part and the second groove part cut alongthe surface orthogonal to the one principal surface of the resonatingarm part and orthogonal to the extension direction of the resonating armpart passes through the middle point of the straight line connecting theone principal surface and the other principal surface, and is not aline-symmetric shape with respect to a center line between the oneprincipal surface and the other principal surface as a straight linealong the one principal surface (other principal surface) as an axis ofsymmetry.

Thereby, under the condition, in the piezoelectric resonator element,mass imbalance is generated in the resonating arm part, and the flexingvibration is vibration formed by synthesizing the original flexingvibration component along the one principal surface and the out-of-planevibration component vibrating in the thickness direction as a directionconnecting the one principal surface and the other principal surface.

As a result, in the piezoelectric resonator element, the vibrationdirection of the flexing vibration is no longer along the specifiedvibration direction, and the loss of vibration energy is generated andthe efficiency of the flexing vibration becomes lower.

On the other hand, in the piezoelectric resonator element, the sectionalshape containing the third groove part and the fourth groove part cutalong the surface orthogonal to the one principal surface of theresonating arm part and orthogonal to the extension direction of theresonating arm part is a shape formed by inverting the sectional shapecontaining the first groove part and the second groove part, and theflexing vibration is vibration formed by synthesizing the originalflexing vibration component along the one principal surface and theout-of-plane vibration component vibrating in the thickness direction asis the case described above.

In this regard, in the piezoelectric resonator element, the sectionalshape containing the third groove part and the fourth groove part is theshape formed by inverting the sectional shape containing the firstgroove part and the second groove part, and thus the direction ofout-of-plane vibration component due to the third groove part and thefourth groove part is opposite to the direction of out-of-planevibration component due to the first groove part and the second groovepart.

As a result, in the piezoelectric resonator element, the out-of-planevibration component due to the first groove part and the second groovepart and the out-of-plane vibration component due to the third groovepart and the fourth groove part are cancelled each other out, and thus,as a whole, the vibration direction of the flexing vibration comescloser to the direction along the one principal surface as the specifiedvibration direction.

Thereby, in the piezoelectric resonator element, the loss of vibrationenergy is suppressed, and the efficiency of the flexing vibration isimproved.

Further, as another aspect, a resonator element includes a base part,and a resonating arm part that extends from the base part in a firstdirection and performs flexing vibration, wherein the resonating armpart has one principal surface and the other principal surface opposedto the one principal surface, a first groove part provided along thefirst direction of the resonating arm part on the one principal surface,a second groove part provided in juxtaposition with the first groovepart in a second direction orthogonal to the first direction in a planview on the other principal surface, a third groove part provided injuxtaposition with the first groove part in the first direction in theplan view and provided nearer the base part side than the first groovepart on the other principal surface, and a fourth groove part providedin juxtaposition with the second groove part in the first direction inthe plan view and provided nearer the base part side than the secondgroove part on the one principal surface, and wherein a sum of a depthof the first groove part and a depth of the second groove part and a sumof a depth of the third groove part and a depth of the fourth groovepart are larger than a distance between the one principal surface andthe other principal surface.

According to the configuration, the resonator element has the firstgroove part on the one principal surface and the second groove partprovided in juxtaposition with the first groove part in the seconddirection on the other principal surface. Further, the resonator elementhas the third groove part provided in juxtaposition with the firstgroove part in the first direction nearer the base part than the firstgroove part on the other principal surface, and the fourth groove partprovided in juxtaposition with the second groove part in the firstdirection nearer the base part than the second groove part on the oneprincipal surface.

Further, in the resonator element, the sum of the depth of the firstgroove part and the depth of the second groove part and the sum of thedepth of the third groove part and the depth of the fourth groove partare larger than the distance between the one principal surface and theother principal surface.

Thereby, in the resonator element, for example, compared to the casewhere groove parts having H-shaped sections are provided in theresonating arm part as in related art, the distance of heat transferfrom one of the pair of contracting and expanding surfaces as acontracting surface in the flexing vibration to the other of the pair ofcontracting and expanding surfaces as an expanding surface is longer,and thus, the relaxation time until the temperature equilibration isachieved becomes longer.

As a result, regarding the resonator element, the frequency of therelaxation oscillation is made farther from the frequency of theoriginal flexing vibration, and the reduction of the Q factor due tothermoelastic loss can be suppressed. Therefore, the resonator elementcan be further downsized.

Now, in the resonator element, the sectional shape containing the firstgroove part and the second groove part cut along the surface orthogonalto the one principal surface of the resonating arm part and orthogonalto the first direction passes through the middle point of the straightline connecting the one principal surface and the other principalsurface, and is not a line-symmetric shape with respect to a center linebetween the one principal surface and the other principal surface as aline along the one principal surface (other principal surface) as anaxis of symmetry.

Thereby, under the condition, in the resonator element, mass imbalanceis generated in the resonating arm part, and the flexing vibration isvibration formed by synthesizing the original flexing vibrationcomponent along the one principal surface and the out-of-plane vibrationcomponent vibrating in the thickness direction as a direction connectingthe one principal surface and the other principal surface.

As a result, in the resonator element, the vibration direction of theflexing vibration is no longer along the specified vibration direction,and the loss of vibration energy is generated and the efficiency of theflexing vibration becomes lower.

On the other hand, in the resonator element, the sectional shapecontaining the third groove part and the fourth groove part cut alongthe surface orthogonal to the one principal surface of the resonatingarm part and orthogonal to the first direction is a shape formed byinverting the sectional shape containing the first groove part and thesecond groove part, and the flexing vibration is vibration formed bysynthesizing the original flexing vibration component along the oneprincipal surface and the out-of-plane vibration component vibrating inthe thickness direction as in the case described above.

In this regard, in the resonator element, the sectional shape containingthe third groove part and the fourth groove part is the shape formed byinverting the sectional shape containing the first groove part and thesecond groove part, and thus, the direction of out-of-plane vibrationcomponent due to the third groove part and the fourth groove part isopposite to the direction of out-of-plane vibration component due to thefirst groove part and the second groove part.

As a result, in the resonator element, the out-of-plane vibrationcomponent due to the first groove part and the second groove part andthe out-of-plane vibration component due to the third groove part andthe fourth groove part are cancelled each other out, and thus, as awhole, the vibration direction of the flexing vibration comes closer tothe direction along one principal surface as the specified vibrationdirection.

Thereby, in the resonator element, the loss of vibration energy issuppressed, and the efficiency of the flexing vibration is improved.

Application Example 2

In the resonator element according to the application example, it ispreferable that, given that lengths of the first groove part and thesecond groove part in the first direction are RS and lengths of thethird groove part and the fourth groove part in the first direction areS, S:RS=1:(2.2 to 2.8).

According to the configuration, in the resonator element, S:RS=1:(2.2 to2.8), and thus, the out-of-plane vibration component due to the firstgroove part and the second groove part and the out-of-plane vibrationcomponent due to the third groove part and the fourth groove part arealmost cancelled each other out.

As a result, in the resonator element, the loss of vibration energy isfurther suppressed and the efficiency of the flexing vibration isfurther improved.

Note that S:RS=1:(2.2 to 2.8) is a finding derived by the inventorsthrough simulations and experiments.

Application Example 3

In the resonator element according to the application example 1, it ispreferable that, given that lengths of the first groove part and thesecond groove part in the first direction are RS, lengths of the thirdgroove part and the fourth groove part in the first direction are S, anda length from a base to a distal end of the resonating arm part is A anda sum of RS and S is L,8.8992×(L/A)²−3.3784×(L/A)+1.746≦RS/S≦1.3102×(L/A)²+3.3784×(L/A)+0.854.

According to the configuration, in the resonator element,8.8992×(L/A)²−3.3784×(L/A)+1.746≦RS/S≦1.3102×(L/A)²+3.3784×(L/A)+0.854,and thus, the out-of-plane vibration component due to the first groovepart and the second groove part and the out-of-plane vibration componentdue to the third groove part and the fourth groove part are almostcancelled each other out.

As a result, in the resonator element, the loss of vibration energy isfurther suppressed and the efficiency of the flexing vibration isfurther improved.

Note that8.8992×(L/A)²−3.3784×(L/A)+1.746≦RS/S≦1.3102×(L/A)²+3.3784×(L/A)+0.854is a finding derived by the inventors through simulations andexperiments.

Application Example 4

In the resonator element according to the application example 3, it ispreferable that RS/S=5.1047×(L/A)²−9×10⁻¹⁴×(L/A)+1.3.

According to the configuration, in the resonator element,RS/S=5.1047×(L/A)²−9×10⁻¹⁴×(L/A)+1.3, and thus, the out-of-planevibration component due to the first groove part and the second groovepart and the out-of-plane vibration component due to the third groovepart and the fourth groove part are almost entirely cancelled each otherout.

As a result, in the resonator element, the loss of vibration energy isfurther suppressed and the efficiency of the flexing vibration isfurther improved.

Note that RS/S=5.1047×(L/A)²−9×10⁻¹⁴×(L/A)+1.3 is a finding derived bythe inventors through simulations and experiments.

Application Example 5

In the resonator element according to the above application example, itis preferable that the resonator element contains quartz.

According to the configuration, the resonator element contains quartz,and thus, a resonator element having advantageous characteristics offrequency-temperature characteristics, processing accuracy, etc. can beprovided because of properties of quartz.

Application Example 6

A resonator according to this application example is a resonator usingthe resonator element according to any one of the application examples 1to 5, and includes the resonator element, and a package housing theresonator element.

According to the configuration, in the resonator, the resonator elementaccording to any one of the application examples 1 to 5 is housed in thepackage, and thus, a resonator that exerts the effect described in anyone of the application examples may be provided.

Application Example 7

An oscillator according to this application example is an oscillatorusing the resonator element according to any one of the applicationexamples 1 to 5, and includes the resonator element, and a circuitdevice that drives the resonator element.

According to the configuration, the oscillator includes the resonatorelement according to any one of the application examples 1 to 5 and thecircuit device, and thus, an oscillator that exerts the effect describedin any one of the application examples may be provided.

Application Example 8

An electronic apparatus according to this application example uses theresonator element according to any one of the application examples 1 to5.

According to the configuration, the electronic apparatus includes theresonator element according to any one of the application examples 1 to5, and thus, an electronic apparatus that exerts the effect described inany one of the application examples 1 to 5 may be provided.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with reference to the accompanyingdrawings, wherein like numbers reference like elements.

FIG. 1 is a schematic perspective view showing an outline configurationof a quartz resonator element of the first embodiment.

FIG. 2 is a schematic plan view of FIG. 1.

FIG. 3A is a sectional view along B-B line of FIG. 2 and wiring diagram,FIG. 3B is a sectional view along C-C line of FIG. 2 and wiring diagram.

FIG. 4 is a graph showing f/fm-dependency of Q factor of a flexingresonator element.

FIG. 5 is a graph showing a correlation between RS/S and UZ/UX(Z-displacement/X-displacement).

FIG. 6 is a graph showing a correlation between L/A and RS/S.

FIG. 7 is a schematic plan view showing a quartz resonator element of amodified example of the first embodiment.

FIG. 8 is a schematic plan view showing an outline configuration of aquartz resonator of the second embodiment.

FIG. 9 is a schematic sectional view of FIG. 8.

FIG. 10 is a schematic sectional view showing an outline configurationof a quartz oscillator of the third embodiment.

FIG. 11 is a schematic perspective view showing a cellular phone of thefourth embodiment.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, embodiments implementing the invention will be describedwith reference to the drawings.

In the first embodiment, a quartz resonator element including quartz asa kind of a piezoelectric material as a resonator element will beexplained as an example. Further, in the second embodiment, the thirdembodiment, and the fourth embodiment, a quartz resonator, a quartzoscillator, and a cellular phone will be explained as examples as aresonator, an oscillator, and an electronic apparatus using the quartzresonator element.

Furthermore, in the following embodiments (except the fourthembodiment), explanation will be made by referring to an X-axis, aY-axis, and a Z-axis, and the respective axes show a crystal X-axis asan electric axis, a crystal Y-axis as a mechanical axis, and a crystalZ-axis as an optical axis as crystal axes of the quartz.

In addition, in the following embodiments, the Z-axis shown in thedrawing may be inclined at 1 degree to 5 degrees relative to the crystalZ-axis, and the plane defined by the Z-axis and the X-axis may be formedat a tilt due to the inclination.

First Embodiment

FIG. 1 is a schematic perspective view showing an outline configurationof a quartz resonator element of the first embodiment. FIG. 2 is aschematic plan view of FIG. 1. FIGS. 3A and 3B are schematic sectionalviews of FIG. 2, and FIG. 3A is a sectional view along B-B line of FIG.2 and wiring diagram and FIG. 3B is a sectional view along C-C line ofFIG. 2 and wiring diagram. Note that, in FIGS. 1 and 2, electrodes andthe like are omitted for convenience.

As shown in FIGS. 1 and 2, a quartz resonator element 1 includes a basepart 10, and a pair of resonating arm parts 20, 21 extending from thebase part 10 in a first direction (Y-axis direction) and performsflexing vibration.

The quartz resonator element 1 forms a tuning fork with the base part 10and the pair of resonating arm parts 20, 21.

The pair of resonating arm parts 20, 21 are formed in rectangular columnshapes, and extend in parallel with each other from one end side of thebase part 10 in the Y-axis direction (first direction).

Note that the base part 10 and the resonating arm parts 20, 21 are cutout from a quartz raw stone or the like, then, ground into a flat plateshape having a predetermined thickness, and formed in an independenttuning fork shape by etching or the like.

The resonating arm parts 20, 21 have one principal surfaces 22, 23 alongthe X-axis direction as a specified vibration direction of the flexingvibration, other principal surfaces 26, 27 facing the one principalsurfaces 22, 23 along the X-axis direction, one surfaces 20 c, 21 c andother surfaces 20 d, 21 d as pairs of expanding and contracting surfacesthat intersect with the X-axis direction and alternately expand andcontract due to the flexing vibration.

The resonating arm parts 20, 21 have first groove parts 24, 25 providedon the one principal surfaces 22, 23 along the extension direction(first direction) of the resonating arm parts 20, 21, and have secondgroove parts 28, 29 provided on the other principal surfaces 26, 27along the second direction (X-axis direction) orthogonal to the firstdirection in a plan view in juxtaposition with the first groove parts24, 25.

Further, the resonating arm parts 20, 21 have third groove parts 24′,25′ provided on the other principal surfaces 26, 27 along the firstdirection in the plan view in juxtaposition with the first groove parts24, 25 and provided nearer the base part 10 side than the first grooveparts 24, 25, and have fourth groove parts 28′, 29′ provided on the oneprincipal surfaces 22, 23 along the first direction in the plan view injuxtaposition with the second groove parts 28, 29 and provided nearerthe base part 10 side than the second groove parts 28, 29.

Note that the one principal surfaces 22, 23 of the resonating arm parts20, 21 are integrated with one principal surface 11 of the base part 10and the other principal surfaces 26, 27 are integrated with the otherprincipal surface 12 of the base part 10.

The third groove parts 24′, 25′ and the fourth groove parts 28′, 29′ areprovided from the bases toward the distal ends of the resonating armparts 20, 21.

Further, as shown in FIG. 2, a predetermined gap G is provided betweenthe third groove parts 24′, 25′ and the fourth groove parts 28′, 29′ andthe first groove parts 24, 25 and the second groove parts 28, 29.

As shown in FIG. 2, in the quartz resonator element 1, given that thelengths of the first groove parts 24, 25 and the second groove parts 28,29 in the extension direction (first direction) are RS and the lengthsof the third groove parts 24′, 25′ and the fourth groove parts 28′, 29′in the extension direction (first direction) are S, it is preferablethat S:RS=1:(2.2 to 2.8), and more preferable that S:RS=1:2.5 (detailswill be described later).

Further, in the quartz resonator element 1, given that the lengths fromthe bases to the distal ends of the resonating arm parts 20, 21 are Aand the sum of RS and S is L, it is preferable that8.8992×(L/A)²−3.3784×(L/A)+1.746≦RS/S≦1.3102×(L/A)²+3.3784×(L/A)+0.854,and more preferable that RS/S=5.1047×(L/A)²−9×10⁻¹⁴×(L/A)+1.3 (detailswill be described later).

As shown in FIGS. 3A and 3B, the first groove parts 24, 25 and thesecond groove parts 28, 29 and the third groove parts 24′, 25′ and thefourth groove parts 28′, 29′ are formed to have nearly rectangularsectional shapes so that the sums of the depths 24 a, 25 a of the firstgroove parts 24, 25 and the depths 28 a, 29 a of the second groove parts28, 29 and the sums of the depths 24 a′, 25 a′ of the third groove parts24′, 25′ and the depths 28 a′ and 29 a′ of the fourth groove parts 28′,29′ may be larger than distances 20 a, 21 a between the one principalsurfaces 22, 23 and the other principal surfaces 26, 27 ((24 a+28 a)>20a, (25 a+29 a)>21 a, (24 a′+28 a′)>20 a, (25 a′+29 a′)>21 a).

Note that the first groove parts 24, 25 and the second groove parts 28,29 and the third groove parts 24′, 25′ and the fourth groove parts 28′,29′ are formed by etching, sandblasting, or the like.

As shown in FIGS. 3A and 3B, on the side walls as outer sides of thefirst groove parts 24, 25 and the second groove parts 28, 29 and thethird groove parts 24′, 25′ and the fourth groove parts 28′, 29′,excitation electrodes 30, 31 are provided.

Specifically, in the resonating arm part 20, the excitation electrodes30 are provided on one surface 20 c connecting the one principal surface22 and the other principal surface 26 and the other surface 20 dconnecting the one principal surface 22 and the other principal surface26.

Further, the excitation electrodes 31 are provided on a surface 24 b atthe one surface 20 c side in the first groove part 24, a surface 28 b atthe other surface 20 d side in the second groove part 28, a surface 24b′ at the one surface 20 c side in the third groove part 24′, and asurface 28 b′ at the other surface 20 d side in the fourth groove part28′.

On the other hand, in the resonating arm part 21, the excitationelectrodes 31 are provided on one surface 21 c connecting the oneprincipal surface 23 and the other principal surface 27 and the othersurface 21 d connecting the one principal surface 23 and the otherprincipal surface 27.

Further, the excitation electrodes 30 are provided on a surface 25 b atthe one surface 21 c side in the first groove part 25, a surface 29 b atthe other surface 21 d side in the second groove part 29, a surface 25b′ at the one surface 21 c side in the third groove part 25′, and asurface 29 b′ at the other surface 21 d side in the fourth groove part29′.

The excitation electrodes 30 are connected to each other andrespectively extracted to the base part 10 by extraction electrodes (notshown) and connected to fixed electrodes (not shown) as well as theexcitation electrodes 31.

Alternating-current charge is applied between the excitation electrodes30 and the excitation electrodes 31.

Note that the excitation electrodes 30, 31 include foundation layers ofCr, Ni, or the like and electrode layers of Au, Ag, or the like. Therespective layers are formed by deposition, sputtering, or the like.

Here, the operation of the quartz resonator element 1 will be explained.

When alternating-current charge is applied between the excitationelectrodes 30, 31 as drive signals, the resonating arm parts 20, 21 ofthe quartz resonator element 1 perform flexing vibration thatalternately displaces in directions of arrows D and in directions ofarrows E nearly along the X-axis direction as shown in FIG. 1.

Specifically, when positive charge is applied to the excitationelectrodes 30 and negative charge is applied to the excitationelectrodes 31, the one surfaces 20 c, 21 c contract in the Y-axisdirection and the other surfaces 20 d, 21 d expand in the Y-axisdirection. Thereby, the resonating arm parts 20, 21 displace in thedirections of the arrows D.

On the other hand, when negative charge is applied to the excitationelectrodes 30 and positive charge is applied to the excitationelectrodes 31, the one surfaces 20 c, 21 c expand in the Y-axisdirection and the other surfaces 20 d, 21 d contract in the Y-axisdirection. Thereby, the resonating arm parts 20, 21 displace in thedirections of the arrows E.

The resonating arm parts 20, 21 of the quartz resonator element 1alternately repeat displacement in the directions of the arrows D and inthe directions of the arrows E, and thereby, the one surfaces 20 c, 21 cand the other surfaces 20 d, 21 d alternately expand and contract.

In this regard, as shown in FIG. 3A, because of the sectional shapes inwhich the first groove parts 24, 25 and the second groove parts 28, 29of the resonating arm parts 20, 21 are formed ((24 a+28 a)>20 a, (25a+29 a)>21 a), the distances of heat transfer from the one surfaces 20c, 21 c to the other surfaces 20 d, 21 d, which alternately repeatexpansion and contraction with the flexing vibration, are longercompared to the case where groove parts having H-shaped sections areprovided as in related art.

Specifically, the distances of heat transfer are a distance from one endat the opening side of the first groove part 24 of the one surface 20 calong the sectional shape to one end at the opening side of the secondgroove part 28 of the other surface 20 d in the resonating arm part 20,and a distance from one end at the opening side of the first groove part25 of the one surface 21 c along the sectional shape to one end at theopening side of the second groove part 29 of the other surface 21 d inthe resonating arm part 21.

Similarly, as shown in FIG. 3B, because of the sectional shapes in whichthe third groove parts 24′, 25′ and the fourth groove parts 28′, 29′ ofthe resonating arm parts 20, 21 are formed ((24 a′+28 a′)>20 a, (25a′+29 a′)>21 a), the distances of heat transfer from the one surfaces 20c, 21 c to the other surfaces 20 d, 21 d, which alternately repeatexpansion and contraction with the flexing vibration, are longercompared to the case where groove parts having H-shaped sections areprovided as in related art.

Here, the frequency f₀ and the relaxation time τ of the above describedrelaxation oscillation are expressed by f₀=1/(2πτ).

Regarding the quartz resonator element 1, the distance of heat transferis longer than that in related art (H-shaped groove part), and therelaxation time τ until the temperature equilibration is achieved islonger than that in related art (H-shaped groove part). As a result,regarding the quartz resonator element 1, the frequency of therelaxation oscillation (relaxation oscillation frequency) f₀ is far fromthe frequency f of the original flexing vibration.

Generally, it is known that the relaxation oscillation frequency(thermal relaxation frequency) f₀ is obtained by the following equation.

f ₀ =πk/(2ρCpa ²)  (1)

Here, π is the ratio of the circumference of a circle to its diameter, kis a coefficient of thermal conductivity of the resonating arm part inthe vibration direction (flexing vibration direction), ρ is mass densityof the resonating arm part, Cp is heat capacity of the resonating armpart, and a is a width of the resonating arm part in the vibrationdirection (flexing vibration direction).

In the case where the coefficient of thermal conductivity k, the massdensity ρ, the heat capacity Cp of the equation (1) are substituted bythe constants of the materials themselves of the resonating arm part,the relaxation oscillation frequency f₀ to be obtained is a relaxationoscillation frequency of the resonating arm part when no groove part isprovided.

FIG. 4 is a graph showing f/fm-dependency of Q factor of the flexingresonator element (quartz resonator element). Here, fm is the relaxationoscillation frequency when no groove part is provided in the resonatingarm part (when the sectional shape of the resonating arm part is anearly rectangular shape). The graphics on the right of the graph inFIG. 4 schematically show the sectional shapes of the resonating armpart.

In FIG. 4, the triangle markers form a plot in the case of the sectionalshape of the resonating arm part shown in FIGS. 3A and 3B, the blacksquare markers form a plot in the H-shaped case where the sectionalshape of the resonating arm part is formed in “H” by providing grooveparts on both principal surfaces of the resonating arm part, and whitediamond markers form a plot in the case of a flat plate when no groovepart is provided in either of the principal surfaces of the resonatingarm part. Further, the thick solid line is an approximate line of thevalues of the triangle markers, the broken line is an interpolation lineof the values of the square markers, and the dashed-dotted line is aninterpolation line of the values of the diamond markers.

As shown in FIG. 4, it becomes clear that, in the flexing resonatorelement, if the sectional shape of the resonating arm part is formed inthe shape shown in FIGS. 3A and 3B and f/fm is a value larger than 0.09,the Q factor higher than that in the case of the H-shape is obtained.

Further, in the above described flexing resonator element (correspondingto the quartz resonator element 1), if f/fm is a value larger than 0.25,the Q factor higher than those in both cases of the H-shape and the flatplate may be obtained, and, if f/fm is a value larger than “1”, the Qfactor significantly higher than those in both cases of the H-shape andthe flat plate may be obtained.

Now, in the quartz resonator element 1, as shown in FIG. 3A, thesectional shapes containing the first groove parts 24, 25 and the secondgroove parts 28, 29 cut along the surface orthogonal to the oneprincipal surfaces 22, 23 of the resonating arm parts 20, 21 andorthogonal to the extension direction (first direction) of theresonating arm parts 20, 21 pass through the middle points of thestraight lines connecting the one principal surfaces 22, 23 and theother principal surfaces 26, 27, and are not line-symmetric shapes withrespect to center lines F, F1 between the one principal surfaces 22, 23and the other principal surfaces 26, 27 as lines along the one principalsurfaces 22, 23 (other principal surfaces 26, 27) as the axes ofsymmetry.

Thereby, under the condition, in the quartz resonator element 1, massimbalance is generated in the resonating arm parts 20, 21, and, as shownin FIG. 3A, the displacement U of the flexing vibration of theresonating arm part 20 becomes a displacement formed by synthesizing thedisplacement component Ux of the original flexing vibration vibrating inthe X-axis direction along the one principal surfaces 22, 23 (otherprincipal surfaces 26, 27) and the displacement component Uz ofout-of-plane vibration vibrating in the Z-axis direction as a directionconnecting the one principal surfaces 22, 23 and the other principalsurfaces 26, 27 by the moment in the Z-axis direction.

On the other hand, the displacement U1 of the flexing vibration of theresonating arm part 21 becomes a displacement formed by synthesizing thedisplacement component U1 x of the original flexing vibration vibratingin the X-axis direction and the displacement component U1 z ofout-of-plane vibration vibrating in the Z-axis direction by the momentin the Z-axis direction.

In this regard, the displacement component Uz and the displacementcomponent U1 z are displacement components in the same direction.

As a result, in the quartz resonator element 1, the directions of thedisplacements U, U1 of the flexing vibration are no longer along the oneprincipal surfaces 22, 23 (no longer along the X-axis direction), andthus, the loss of vibration energy may be generated and the efficiencyof the flexing vibration may become lower.

Note that, in FIG. 3A, the displacements U, U1 in one direction of theflexing vibration (corresponding to the directions of arrows D inFIG. 1) are shown for convenience, however, the same is applicable tothe displacements in the opposite direction (corresponding to thedirections of arrows E in FIG. 1).

On the other hand, in the quartz resonator element 1, as shown in FIG.3B, the sectional shapes containing the third groove parts 24′, 25′ andthe fourth groove parts 28′, 29′ cut along the surface orthogonal to theone principal surfaces 22, 23 of the resonating arm parts 20, 21 andorthogonal to the extension direction (first direction) of theresonating arm parts 20, 21 are shapes formed by inverting the sectionalshapes containing the first groove parts 24, 25 and the second grooveparts 28, 29.

Thereby, in the quartz resonator element 1, in the third groove parts24′, 25′ and the fourth groove parts 28′, 29′, the displacements U′, U1′of the flexing vibration become displacements formed by synthesizing thedisplacement components Ux′, U1 x′ of the original flexing vibrationalong the one principal surfaces 22, 23 and the displacement componentsUz′, U1 z′ of out-of-plane vibration vibrating in the Z-axis directionas in the case described above.

In this regard, in the quartz resonator element 1, the sectional shapescontaining the third groove parts 24′, 25′ and the fourth groove parts28′, 29′ are shapes formed by inverting the sectional shapes containingthe first groove parts 24, 25 and the second groove parts 28, 29, andthus, the directions of the displacement components Uz′, U1 z′ ofout-of-plane vibration in the third groove parts 24′, 25′ and the fourthgroove parts 28′, 29′ are opposite to the directions of the displacementcomponents Uz, U1 z of out-of-plane vibration in the first groove parts24, 25 and the second groove parts 28, 29.

As a result, in the quartz resonator element 1, the displacementcomponents Uz, U1 z of out-of-plane vibration in the first groove parts24, 25 and the second groove parts 28, 29 and the displacementcomponents Uz′, U1 z′ of out-of-plane vibration in the third grooveparts 24′, 25′ and the fourth groove parts 28′, 29′ are cancelled eachother out, and thus, as a whole, the directions of the displacements ofthe flexing vibration come closer to the X-axis direction (thedirections along one principal surfaces) as the specified vibrationdirection.

Thereby, in the quartz resonator element 1, the moment in theZ-direction decreases and the loss of vibration energy is suppressed,and the efficiency of the flexing vibration is improved.

The above description will be further explained based on specific data.

FIG. 5 is a graph showing a correlation between a ratio of lengths RS ofthe first groove parts 24, 25 and the second groove parts 28, 29 in theextension direction to the lengths S of the third groove parts 24′, 25′and the fourth groove parts 28′, 29′ in the extension direction(hereinafter, may simply be referred to as RS/S) and a ratio of thedisplacement component UZ of out-of-plane vibration (vibration in theZ-axis direction) in the flexing vibration of the quartz resonatorelement 1 as a whole to the displacement component UX in the X-axisdirection as the originally specified vibration direction (hereinafter,may simply be referred to as UZ/UX).

FIG. 6 is a graph showing a correlation between a ratio of the sums L(RS+S) of the lengths of the respective groove parts at the distal endside and the base part side of the resonating arm parts 20, 21 to thelengths A from the bases to the distal ends of the resonating arm parts20, 21 (hereinafter, may simply be referred to as L/A) and RS/S withwhich the loss of vibration energy is within an allowable range.

FIGS. 5 and 6 are based on data derived by the inventors throughsimulations and experiments.

As shown in FIG. 5, regarding the quartz resonator element 1, whenRS/S=2.2 to 2.8, i.e., S:RS=1:(2.2 to 2.8), UZ/UX becomes smaller, and avalue of vibration leakage Δf (a shift amount between the frequency whenthe base part 10 is hung with wires or fixed with a soft conductingadhesive and the frequency when the base part 10 is fixed with solder ora hard conducting adhesive) as one scale of the loss of vibration energyin the flexing vibration becomes smaller. Specifically, the vibrationleakage Δf becomes about 500 ppm or less at the appropriate level formass production.

Further, regarding the quartz resonator element 1, when RS/S=2.5, i.e.,S:RS=1:2.5, UZ/UX becomes nearly zero, and the value of the vibrationleakage Δf becomes the minimum (nearly 0 ppm).

The negative sign of UZ/UX shows that the displacement direction ofout-of-plane vibration becomes opposite (from the positive direction ofthe Z-axis to the negative direction of the Z-axis).

As shown in FIG. 6, regarding the quartz resonator element 1, when8.8992×(L/A)²−3.3784×(L/A)+1.746 (the lowermost line in thedrawing)≦RS/S≦1.3102×(L/A)²+3.3784×(L/A)+0.854 (the uppermost line inthe drawing), UZ/UX becomes smaller, and the value of the vibrationleakage Δf becomes smaller. Specifically, the leakage becomes about 500ppm or less at the appropriate level for mass production.

Furthermore, regarding the quartz resonator element 1, whenRS/S=5.1047×(L/A)²−9×10⁻¹⁴×(L/A)+1.3 (the center line in the drawing),UZ/UX becomes nearly zero, and the value of the vibration leakage Δfbecomes the minimum (nearly 0 ppm).

Note that, in the simulations and the experiments, using samples havingthe lengths A=about 1650 μm from the bases to the distal ends of theresonating arm parts 20, 21 and the widths W=about 100 μm of theresonating arm parts 20, 21 in the X-axis direction, they are fixed at agap G=about 20 μm, the values of RS, S, L are appropriately set inranges of RS=about 200 μm to about 1100 μm, S=about 100 μm to about 600μm, and L=about 400 μm to about 1200 μm, and evaluations are made.

As described above, in the quartz resonator element 1 of the firstembodiment, the sums of the depths 24 a, 25 a of the first groove parts24, 25 and the depths 28 a, 29 a of the second groove parts 28, 29 andthe sums of the depths 24 a′, 25 a′ of the third groove parts 24′, 25′and the depths 28 a′ and 29 a′ of the fourth groove parts 28′, 29′ arelarger than distances 20 a, 21 a between the one principal surfaces 22,23 and the other principal surfaces 26, 27 ((24 a+28 a)>20 a, (25 a+29a)>21 a, (24 a′+28 a′)>20 a, (25 a′+29 a′)>21 a).

Thereby, in the quartz resonator element 1, the distances of heattransfer from the contracting surfaces to the expanding surfaces (thedistances of heat transfer from the one surfaces 20 c, 21 c to the othersurfaces 20 d, 21 d) in the flexing vibration are longer compared to thecase where groove parts having H-shaped sections are provided as inrelated art in the resonating arm parts 20, 21, for example, and thus,the relaxation time τ until the temperature equilibration is achievedbecomes longer.

As a result, regarding the quartz resonator element 1, the relaxationoscillation frequency f₀ is made farther from the frequency f of theoriginal flexing vibration, and the reduction of the Q factor due tothermoelastic loss can be suppressed. Therefore, the quartz resonatorelement 1 can be further downsized.

Further, in the quartz resonator element 1, the sectional shapescontaining the third groove parts 24′, 25′ and the fourth groove parts28′, 29′ cut along the surface orthogonal to the one principal surfaces22, 23 of the resonating arm parts 20, 21 and orthogonal to theextension direction (first direction) of the resonating arm parts 20,are shapes formed by inverting the sectional shapes containing the firstgroove parts 24, 25 and the second groove parts 28, 29 cut in thesimilar manner.

Thereby, in the quartz resonator element 1, the directions of thedisplacement components Uz, U1 z of out-of-plane vibration due to thefirst groove parts 24, 25 and the second groove parts 28, 29 in theflexing vibration and the directions of the displacement components Uz′,U1 z′ of out-of-plane vibration due to the third groove parts 24′, 25′and the fourth groove parts 28′, 29′ are opposite.

As a result, in the quartz resonator element 1, the displacementcomponents Uz, U1 z of out-of-plane vibration due to the first grooveparts 24, 25 and the second groove parts 28, 29 and the displacementcomponents Uz′, U1 z′ of out-of-plane vibration due to the third grooveparts 24′, 25′ and the fourth groove parts 28′, 29′ are cancelled eachother out, and thus, as a whole, the vibration direction of the flexingvibration comes closer to the X-axis direction (the direction along oneprincipal surfaces 22, 23) as the specified vibration direction.

Thereby, in the quartz resonator element 1, the loss of vibration energyin the flexing vibration is suppressed, and thus, the CI (crystalimpedance) value or the like becomes lower and the efficiency of theflexing vibration is improved.

Further, regarding the quartz resonator element 1, when S:RS=1:(2.2 to2.8), the displacement components Uz, U1 z of out-of-plane vibration dueto the first groove parts 24, 25 and the second groove parts 28, 29 andthe displacement components Uz′, U1 z′ of out-of-plane vibration due tothe third groove parts 24′, 25′ and the fourth groove parts 28′, 29′ arealmost cancelled each other out.

As a result, in the quartz resonator element 1, UZ/UX becomes smaller,and the value of the vibration leakage Δf as the loss of vibrationenergy becomes even smaller (about 500 ppm or less) and the efficiencyof the flexing vibration is further improved.

Furthermore, regarding the quartz resonator element 1, when S:RS=1:2.5,the displacement components Uz, U1 z of out-of-plane vibration due tothe first groove parts 24, 25 and the second groove parts 28, 29 and thedisplacement components Uz′, U1 z′ of out-of-plane vibration due to thethird groove parts 24′, 25′ and the fourth groove parts 28′, 29′ arealmost entirely cancelled each other out.

As a result, in the quartz resonator element 1, the UZ/UX becomes nearlyzero, and the value of the vibration leakage Δf becomes the minimum(nearly 0 ppm) and the efficiency of the flexing vibration is furtherimproved.

Further, regarding the quartz resonator element 1, when8.8992×(L/A)²−3.3784×(L/A)+1.746≦RS/S≦1.3102×(L/A)²+3.3784×(L/A)+0.854,the displacement components Uz, U1 z of out-of-plane vibration due tothe first groove parts 24, 25 and the second groove parts 28, 29 and thedisplacement components Uz′, U1 z′ of out-of-plane vibration due to thethird groove parts 24′, 25′ and the fourth groove parts 28′, 29′ arealmost cancelled each other out.

As a result, in the quartz resonator element 1, UZ/UX becomes smaller,and the value of the vibration leakage Δf becomes even smaller (about500 ppm or less), the efficiency of the flexing vibration is furtherimproved.

Furthermore, regarding the quartz resonator element 1, whenRS/S=5.1047×(L/A)²−9×10⁻¹⁴×(L/A)+1.3, the displacement components Uz, U1z of out-of-plane vibration due to the first groove parts 24, 25 and thesecond groove parts 28, 29 and the displacement components Uz′, U1 z′ ofout-of-plane vibration due to the third groove parts 24′, 25′ and thefourth groove parts 28′, 29′ are further cancelled each other out.

As a result, in the quartz resonator element 1, UZ/UX becomes nearlyzero, and the value of the vibration leakage Δf becomes the minimum(nearly 0 ppm) and the efficiency of the flexing vibration is furtherimproved.

In addition, since the quartz resonator element 1 contains quarts, itmay be provided as a resonator element having advantageouscharacteristics of frequency-temperature characteristics, agingcharacteristics of frequency, processing accuracy, etc. because ofproperties of quartz.

Modified Example

As below, a modified example of the quartz resonator element of thefirst embodiment will be explained.

FIG. 7 is a schematic plan view showing a quartz resonator element of amodified example of the first embodiment. The same signs are assigned tothe common parts with the first embodiment and their explanation will beomitted, and the parts different from those of the first embodiment willbe explained mainly.

As shown in FIG. 7, in a quartz resonator element 101, the arrangementof the first groove part 25 and the second groove part 29 and the thirdgroove part 25′, and the fourth groove part 29′ in a resonating arm part121 is reversed compared to the arrange of those of the resonating armpart 21 of the quartz resonator element 1 in the embodiment. In otherwords, in the quartz resonator element 101, the arrangement of therespective groove parts is the same in the resonating arm part 20 andthe resonating arm part 121.

The quartz resonator element 101 may exert the same effect as that ofthe first embodiment by the same operation as that of the firstembodiment in the arrangement.

Note that, in the above described embodiment and modified example, thetuning fork-type quartz resonator element having the pair of resonatingarm parts has been explained as an example, however, not limited tothat, but, for example, a rod-like quartz resonator element having oneresonating arm part or a tuning fork-type quartz resonator elementhaving three or more resonating arm parts may be used.

Second Embodiment

As below, a quartz resonator as a resonator of the second embodimentwill be explained as an example.

FIG. 8 is a schematic plan view showing an outline configuration of aquartz resonator of the second embodiment. FIG. 9 is a schematicsectional view along J-J line of FIG. 8. In FIG. 8, a lid body isomitted for convenience.

Further, the same signs are assigned to the common parts with the firstembodiment and their explanation will be omitted.

The quartz resonator 80 of the second embodiment is a quartz resonatorusing the quartz resonator element of the first embodiment or themodified example of the first embodiment. Here, the explanation will bemade using the quartz resonator element 1 of the first embodiment.

As shown in FIGS. 8, 9, the quartz resonator 80 houses the quartzresonator element 1 within a package 51. Specifically, the quartzresonator 80 houses the quartz resonator element 1 in an internal spaceS of the package 51 including a first substrate 54, and a secondsubstrate 55 and a third substrate 56 stacked on the first substrate 54.

The package 51 includes the first substrate 54, the second substrate 55,and the third substrate 56, and further includes a lid body 57. In thepackage 51, the second substrate 55 has an extension part 55 a extendedwithin the package 51, and two electrode parts 52 are formed in theextension part 55 a.

In the quartz resonator 80, fixed electrodes (not shown) of the quartzresonator element 1 are fixed to the electrode parts 52 using conductingadhesives 53 or the like, and the excitation electrodes 30, 31 (seeFIGS. 3A and 3B) and the electrode parts 52 are electrically connectedvia the fixed electrodes. As the conducting adhesives 53, materialsformed by adding conducting particles such as silver particles to bindercomponents of a predetermined synthetic resin may be used.

The first substrate 54, the second substrate 55, and the third substrate56 are formed by an insulating material such as ceramic. Specifically,as a preferable material, a material having a linear coefficient ofexpansion equal or approximate to that of the quartz resonator element 1or the lid body 57 is selected.

In the embodiment, for example, a green sheet of ceramic is used. Thegreen sheet is obtained, for example, by dispersing ceramic powder in apredetermined solution, adding a binder thereto, shaping the producedkneaded material into an elongated sheet, and cutting this intopredetermined lengths.

The first substrate 54, the second substrate 55, and the third substrate56 may be formed by stacking and sintering the green sheets shaped inthe shapes as shown in the drawings. The first substrate 54 forms thebottom part of the package 51 and the second substrate 55 and the thirdsubstrate 56 stacked thereon are formed in frame shapes to form theinternal space S with the first substrate 54 and the lid body 57.

To the third substrate 56, the lid body 57 formed by ceramic, glass or ametal such as kovar is joined via a joining material 58 such as a kovarring or low-melting-point glass. Thereby, the internal space S of thepackage 51 is air-tightly sealed.

On the first substrate 54, the above described electrode parts 52 areformed, for example, by forming a conducting pattern (not shown) using aconducting paste of AG, Pd, or the like or a conducting paste oftungsten metalize or the like, then, sintering the first substrate 54,the second substrate 55, and the third substrate 56, and then,sequentially plating Ni, Au or Ag, etc.

The electrode parts 52 are electrically connected to a mounted terminal59 formed on the outer bottom surface of the package 51 by theconducting pattern (not shown).

In the quartz resonator 80, by applying a drive signal to the mountedterminal 59, alternating-current charge is applied between theexcitation electrodes 30, 31 of the quartz resonator element 1 via thefixed electrodes (see FIGS. 3A and 3B).

Thereby, the quartz resonator element 1 performs the flexing vibrationas shown in FIG. 1.

As described above, in the quartz resonator 80, the quartz resonatorelement 1 is housed in the internal space S of the package 51 and theinternal space S of the package 51 is air-tightly sealed, and thus, theresonator that exerts the same effect as that of the first embodimentmay be provided.

Note that, in the quartz resonator 80, even if the quartz resonatorelement 101 of the modified example of the first embodiment is used inplace of the quartz resonator element 1, the resonator that exerts thesame effect as that of the first embodiment may be provided.

In the quartz resonator 80, the second substrate 55 and the thirdsubstrate 56 may be omitted by forming the lid body 57 in a flanged capshape. Thereby, in the quartz resonator 80, the number of componentelements is smaller and the manufacturing of the package 51 becomeseasier.

Third Embodiment

As below, a quartz oscillator as an oscillator of the third embodimentwill be explained as an example.

FIG. 10 is a schematic sectional view showing an outline configurationof the quartz oscillator of the third embodiment.

A quartz oscillator 90 of the third embodiment is a quartz oscillatorusing the quartz resonator element of the first embodiment or themodified example of the first embodiment. Here, the explanation will bemade using the quartz resonator element 1 of the first embodiment. Thequartz oscillator 90 of the third embodiment includes an IC chip 87 as acircuit device that drives the quartz resonator element 1 in addition tothe quartz resonator 80 of the second embodiment.

The same signs are assigned to the common parts with the firstembodiment and the second embodiment and their explanation will beomitted.

As shown in FIG. 10, in the quartz oscillator 90, an internal connectingterminal 89 including Au etc. is formed on the upper surface of thefirst substrate 54 of the package 51.

The IC chip 87 having an oscillation circuit inside is housed in theinternal space S of the package 51, and fixed to the upper surface ofthe first substrate 54 using an adhesive or the like. Further, on theupper surface of the IC chip 87, an IC connecting pad 82 including Auetc. is formed.

The IC connecting pad 82 is connected to the internal connectingterminal 89 using a metal wire 88.

The internal connecting terminal 89 is connected to the mounted terminal59 formed on the outer bottom surface and the electrode parts 52 via theconducting pattern (not shown). A connecting method using flip-chipmounting other than the connecting method using the metal wire 88 may beused for the connection between the IC chip 87 and the internalconnecting terminal 89.

The internal space S of the package 51 is air-tightly sealed.

In the quartz oscillator 90, alternating-current charge is appliedbetween the excitation electrodes 30, 31 of the quartz resonator element1 from the IC chip 87 via the electrode parts 52 and the fixedelectrodes (not shown) by external input (see FIGS. 3A and 3B).

Thereby, the quartz resonator element 1 performs the flexing vibrationas shown in FIG. 1. The quartz oscillator 90 outputs the oscillationsignals obtained by the flexing vibration to the outside via the IC chip87 and the mounted terminal 59.

As described above, in the quartz oscillator 90 of the third embodiment,the quartz resonator element 1 and the IC chip 78 are housed in theinternal space S of the package 51 and the internal space S of thepackage 51 is air-tightly sealed, and thus, the resonator that exertsthe same effect as that of the first embodiment may be provided.

Note that, in the quartz oscillator 90, even if the quartz resonatorelement 101 of the modified example of the first embodiment is used inplace of the quartz resonator element 1, the resonator that exerts thesame effect as that of the first embodiment may be provided.

The quartz oscillator 90 may have a configuration in which the IC chip87 is attached to the outside of the package 51 (module structure).

In the third embodiment, the quartz oscillator has been explained as anexample, however, not limited to that, but, for example, a pressuresensor, a gyro sensor, or the like further including a detection circuitin the IC chip 87 may be used.

Fourth Embodiment

As below, a cellular phone as an electronic apparatus of the fourthembodiment will be explained as an example.

FIG. 11 is a schematic perspective view showing the cellular phone ofthe fourth embodiment.

The cellular phone 700 of the fourth embodiment is a cellular phoneusing the quartz resonator element of the first embodiment or themodified example of the first embodiment.

The cellular phone 700 shown in FIG. 11 uses the above described quartzresonator element 1 (101) as a reference clock oscillation source, forexample, and further includes a liquid crystal display device 701,plural operation buttons 702, an earpiece 703, and a mouth piece 704.

The above described quartz resonator element 1 (101) may preferably beused as a reference clock oscillation source not only of the cellularphone but also an electronic book, a personal computer, a television, adigital still camera, a video camera, a video recorder, a car navigationdevice, a pager, an electronic organizer, an electronic calculator, aword processor, a work station, a videophone, a POS terminal, and adevice having a touch panel, and, in any case, an electronic apparatusthat exerts the effect explained in the embodiment and the modifiedexample may be provided.

As a material of the resonator element, not limited to quartz, but apiezoelectric material such as lithium tantalate (LiTaO₃), lithiumtetraborate (Li₂B₄O₇), lithium niobate (LiNbO₃), lead zirconate titanate(PZT), zinc oxide (ZnO), or aluminum nitride (AlN), or a semiconductorsuch as silicon having a piezoelectric material such as zinc oxide (ZnO)or aluminum nitride (AlN) as a coating may be used.

The entire disclosure of Japanese Patent Application No. 2009-229290,filed Oct. 1, 2009 and No. 2010-167853, filed Jul. 27, 2010 areexpressly incorporated by reference herein.

1. A resonator element comprising: a base part; and a resonating armpart that extends from the base part in a first direction and performsflexing vibration, wherein the resonating arm part has one principalsurface and the other principal surface opposed to the one principalsurface, a first groove part provided along the first direction of theresonating arm part on the one principal surface, a second groove partprovided in juxtaposition with the first groove part in a seconddirection orthogonal to the first direction in a plan view on the otherprincipal surface, a third groove part provided in juxtaposition withthe first groove part in the first direction in the plan view andprovided nearer the base part side than the first groove on the otherprincipal surface, and a fourth groove part provided in juxtapositionwith the second groove part in the first direction in the plan view andprovided nearer the base part side than the second groove on the oneprincipal surface, and wherein a sum of a depth of the first groove partand a depth of the second groove part and a sum of a depth of the thirdgroove part and a depth of the fourth groove part are larger than adistance between the one principal surface and the other principalsurface.
 2. The resonator element according to claim 1, wherein, giventhat lengths of the first groove part and the second groove part in thefirst direction are RS and lengths of the third groove part and thefourth groove part in the first direction are S, S:RS=1:(2.2 to 2.8). 3.The resonator element according to claim 1, wherein, given that lengthsof the first groove part and the second groove part in the firstdirection are RS, lengths of the third groove part and the fourth groovepart in the first direction are S, a length from a base to a distal endof the resonating arm part is A, and a sum of RS and S is L,8.8992×(L/A)²−3.3784×(L/A)+1.746≦RS/S≦1.3102×(L/A)²+3.3784×(L/A)+0.854.4. The resonator element according to claim 3, whereinRS/S=5.1047×(L/A)²−9×10⁻¹⁴×(L/A)+1.3.
 5. The resonator element accordingto claim 1, wherein the resonator element contains quartz.
 6. Aresonator using the resonator element according to claim 1, comprising:the resonator element; and a package housing the resonator element. 7.An oscillator using the resonator element according to claim 1,comprising: the resonator element; and a circuit device that drives theresonator element.
 8. An electronic apparatus using the resonatorelement according to claim 1.